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 A306080 Expansion of e.g.f. Product_{k>=1} (1 + (exp(x) - 1)^k)^k. 2
 1, 1, 5, 43, 401, 4651, 64265, 1015603, 17996081, 354373531, 7682286425, 181466541763, 4632985312961, 127068851847211, 3724903637434985, 116185013450349523, 3840969677266089041, 134113334651486325691, 4930511086446971405945, 190327859758408148070883 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..410 Vaclav Kotesovec, Graph - The asymptotic ratio FORMULA a(n) = Sum_{k=0..n} Stirling2(n,k) * A026007(k) * k!. a(n) ~ n! * exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / (4 * log(2)^(2/3)) + (1 - log(2)) * (3*Zeta(3))^(2/3) * n^(1/3) / (8 * log(2)^(4/3)) - (log(2)^2 + log(2) - 1) * Zeta(3) / (16 * log(2)^2)) * Zeta(3)^(1/6) / (2^(13/12) * 3^(1/3) * sqrt(Pi) * n^(2/3) * (log(2))^(n + 1/3)). - Vaclav Kotesovec, Jun 23 2018 MATHEMATICA nmax = 20; CoefficientList[Series[Product[(1 + (Exp[x] - 1)^k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! CROSSREFS Cf. A026007, A305550, A306046, A306081. Sequence in context: A326884 A241707 A322246 * A156886 A112115 A350117 Adjacent sequences: A306077 A306078 A306079 * A306081 A306082 A306083 KEYWORD nonn AUTHOR Vaclav Kotesovec, Jun 20 2018 STATUS approved

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Last modified September 19 09:52 EDT 2024. Contains 376008 sequences. (Running on oeis4.)